In my current WIP, I use the stats screen as an, ‘any time, any place, all-access do-as-you-please’. The stats screen gives you the opportunity do many things that aren’t considered ‘canon’, like you can access your quests, view your relationships, your skills, it lets you take notes as you please, edit the game mechanics (i.e. enable/disable flavour text, adjust difficulty, change the character gender, re-allocate investments, etc.).
I think that the stats screen can be viewed either as part of the narrative world, or as a pause button that takes you out of the game. I interpret mine as a ‘take pause an view where we’re at in this crazy world’ kind of thing.
Regardless, I think it is important to consider that your stat screen is essentially a menu - if your player wants to change their gender, get a recap of what they’ve been doing, want to view their inventory, or anything that doesn’t necessarily have a natural place in the actual narrative, the Stat Screen is the easy-access go to, similar to hitting the pause button on a game.
If you’re feeling adventurous, it’s always interesting to have the stats screen actually affect the game in small ways. If you’ve read another character’s bio in your stats screen, maybe you can gain the upper hand by unlocking a choice option in the narrative.
As for which stats you want to use, that’s more a personal choice. I prefer to keep all the specific mechanics hidden. I don’t show percentages, or numbers, but I give general indications of things.
I hope this helps somewhat to inspire you.